{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple Comparisons"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_This setup code is required to run in an IPython notebook_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.simplefilter('ignore')\n",
    "\n",
    "# Reproducability\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "\n",
    "seaborn.set_style('darkgrid')\n",
    "plt.rc(\"figure\", figsize=(16, 6))\n",
    "plt.rc(\"savefig\", dpi=90)\n",
    "plt.rc(\"font\",family=\"sans-serif\")\n",
    "plt.rc(\"font\",size=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.random.seed(23456)\n",
    "# Common seed used throughout\n",
    "seed = np.random.randint(0, 2**31 - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The multiple comparison procedures all allow for examining aspects of superior predictive ability. There are three available:\n",
    "\n",
    "* `SPA` - The test of Superior Predictive Ability, also known as the Reality Check (and accessible as `RealityCheck`) or the bootstrap data snooper, examines whether any model in a set of models can outperform a benchmark.\n",
    "* `StepM` - The stepwise multiple testing procedure uses sequential testing to determine which models are superior to a benchmark.\n",
    "* `MCS` - The model confidence set which computes the set of models which with performance indistinguishable from others in the set.\n",
    "\n",
    "All procedures take **losses** as inputs.  That is, smaller values are preferred to larger values.  This is common when evaluating forecasting models where the loss function is usually defined as a positive function of the forecast error that is increasing in the absolute error.  Leading examples are Mean Square Error (MSE) and Mean Absolute Deviation (MAD)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The test of Superior Predictive Ability (SPA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This procedure requires a $t$-element array of benchmark losses and a $t$ by $k$-element array of model losses.  The null hypothesis is that no model is better than the benchmark, or \n",
    "\n",
    "$$ H_0: \\max_i E[L_i] \\geq E[L_{bm}] $$\n",
    "\n",
    "where $L_i$ is the loss from model $i$ and $L_{bm}$ is the loss from the benchmark model.\n",
    "\n",
    "This procedure is normally used when there are many competing forecasting models such as in the study of technical trading rules.  The example below will make use of a set of models which are all equivalently good to a benchmark model and will serve as a *size study*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Study Design"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The study will make use of a measurement error in predictors to produce a large set of correlated variables that all have equal expected MSE.  The benchmark will have identical measurement error and so all models have the same expected loss, although will have different forecasts.\n",
    "\n",
    "The first block computed the series to be forecast."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import randn\n",
    "import statsmodels.api as sm\n",
    "\n",
    "t = 1000\n",
    "factors = randn(t, 3)\n",
    "beta = np.array([1, 0.5, 0.1])\n",
    "e = randn(t)\n",
    "y = factors.dot(beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next block computes the benchmark factors and the model factors by contaminating the original factors with noise.  The models are estimated on the first 500 observations and predictions are made for the second 500.  Finally, losses are constructed from these predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Measurement noise\n",
    "bm_factors = factors + randn(t, 3)\n",
    "# Fit using first half, predict second half\n",
    "bm_beta = sm.OLS(y[:500], bm_factors[:500]).fit().params\n",
    "# MSE loss\n",
    "bm_losses = (y[500:] - bm_factors[500:].dot(bm_beta))**2.0\n",
    "# Number of models\n",
    "k = 500\n",
    "model_factors = np.zeros((k, t, 3))\n",
    "model_losses = np.zeros((500, k))\n",
    "for i in range(k):\n",
    "    # Add measurement noise\n",
    "    model_factors[i] = factors + randn(1000, 3)\n",
    "    # Compute regression parameters\n",
    "    model_beta = sm.OLS(y[:500], model_factors[i, :500]).fit().params\n",
    "    # Prediction and losses\n",
    "    model_losses[:, i] = (\n",
    "        y[500:] - model_factors[i, 500:].dot(model_beta))**2.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally the SPA can be used.  The SPA requires the **losses** from the benchmark and the models as inputs.  Other inputs allow the bootstrap sued to be changed or for various options regarding studentization of the losses.  `compute` does the real work, and then `pvalues` contains the probability that the null is true given the realizations.\n",
    "\n",
    "In this case, one would not reject. The three p-values correspond to different re-centerings of the losses.  In general, the `consistent` p-value should be used.  It should always be the case that\n",
    "\n",
    "$$ lower \\leq consistent \\leq upper .$$\n",
    "\n",
    "See the original papers for more details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "lower         0.520\n",
       "consistent    0.723\n",
       "upper         0.733\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from arch.bootstrap import SPA\n",
    "\n",
    "spa = SPA(bm_losses, model_losses)\n",
    "spa.seed(seed)\n",
    "spa.compute()\n",
    "spa.pvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same blocks can be repeated to perform a simulation study.  Here I only use 100 replications since this should complete in a reasonable amount of time.  Also I set `reps=250` to limit the number of bootstrap replications in each application of the SPA (the default is a more reasonable 1000)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "10\n",
      "20\n",
      "30\n",
      "40\n",
      "50\n",
      "60\n",
      "70\n",
      "80\n",
      "90\n"
     ]
    }
   ],
   "source": [
    "# Save the pvalues\n",
    "pvalues = []\n",
    "b = 100\n",
    "seeds = np.random.randint(0, 2**31 - 1, b)\n",
    "# Repeat 100 times\n",
    "for j in range(b):\n",
    "    if j % 10 == 0:\n",
    "        print(j)\n",
    "    factors = randn(t, 3)\n",
    "    beta = np.array([1, 0.5, 0.1])\n",
    "    e = randn(t)\n",
    "    y = factors.dot(beta)\n",
    "\n",
    "    # Measurement noise\n",
    "    bm_factors = factors + randn(t, 3)\n",
    "    # Fit using first half, predict second half\n",
    "    bm_beta = sm.OLS(y[:500], bm_factors[:500]).fit().params\n",
    "    # MSE loss\n",
    "    bm_losses = (y[500:] - bm_factors[500:].dot(bm_beta))**2.0\n",
    "    # Number of models\n",
    "    k = 500\n",
    "    model_factors = np.zeros((k, t, 3))\n",
    "    model_losses = np.zeros((500, k))\n",
    "    for i in range(k):\n",
    "        model_factors[i] = factors + randn(1000, 3)\n",
    "        model_beta = sm.OLS(y[:500], model_factors[i, :500]).fit().params\n",
    "        # MSE loss\n",
    "        model_losses[:, i] = (\n",
    "            y[500:] - model_factors[i, 500:].dot(model_beta))**2.0\n",
    "    # Lower the bootstrap replications to 250\n",
    "    spa = SPA(bm_losses, model_losses, reps=250)\n",
    "    spa.seed(seeds[j])\n",
    "    spa.compute()\n",
    "    pvalues.append(spa.pvalues)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally the pvalues can be plotted.  Ideally they should form a $45^o$ line indicating the size is correct.  Both the consistent and upper perform well.  The lower has too many small p-values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "pvalues = pd.DataFrame(pvalues)\n",
    "for col in pvalues:\n",
    "    values = pvalues[col].values\n",
    "    values.sort()\n",
    "    pvalues[col] = values\n",
    "# Change the index so that the x-values are between 0 and 1\n",
    "pvalues.index = np.linspace(0.005, .995, 100)\n",
    "fig = pvalues.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Power"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The SPA also has power to reject then the null is violated.  The simulation will be modified so that the amount of measurement error differs across models, and so that some models are actually better than the benchmark.   The p-values should be small indicating rejection of the null."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "lower         0.0\n",
       "consistent    0.0\n",
       "upper         0.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Number of models\n",
    "k = 500\n",
    "model_factors = np.zeros((k, t, 3))\n",
    "model_losses = np.zeros((500, k))\n",
    "for i in range(k):\n",
    "    scale = ((2500.0 - i) / 2500.0)\n",
    "    model_factors[i] = factors + scale * randn(1000, 3)\n",
    "    model_beta = sm.OLS(y[:500], model_factors[i, :500]).fit().params\n",
    "    # MSE loss\n",
    "    model_losses[:, i] = (\n",
    "        y[500:] - model_factors[i, 500:].dot(model_beta))**2.0\n",
    "\n",
    "spa = SPA(bm_losses, model_losses)\n",
    "spa.seed(seed)\n",
    "spa.compute()\n",
    "spa.pvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the average losses are plotted.  The higher index models are clearly better than the lower index models -- and the benchmark model (which is identical to model.0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_losses = pd.DataFrame(\n",
    "    model_losses, columns=['model.' + str(i) for i in range(k)])\n",
    "avg_model_losses = pd.DataFrame(model_losses.mean(0), columns=['Average loss'])\n",
    "fig = avg_model_losses.plot(style=['o'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stepwise Multiple Testing (StepM)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Stepwise Multiple Testing is similar to the SPA and has the same null. The primary difference is that it identifies the set of models which are better than the benchmark, rather than just asking the basic question if any model is better.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model indices:\n",
      "['106', '115', '117', '152', '156', '157', '158', '169', '186', '187', '192', '197', '214', '215', '219', '228', '235', '238', '246', '248', '252', '253', '254', '257', '261', '262', '263', '266', '272', '275', '279', '280', '281', '282', '286', '291', '294', '298', '299', '300', '305', '306', '310', '312', '316', '318', '325', '326', '329', '330', '332', '335', '336', '338', '340', '341', '342', '344', '348', '349', '350', '351', '352', '353', '354', '356', '357', '359', '360', '362', '363', '364', '365', '367', '368', '370', '371', '372', '373', '374', '377', '378', '379', '380', '382', '383', '385', '386', '387', '388', '389', '390', '391', '392', '393', '394', '395', '398', '399', '400', '401', '402', '403', '404', '405', '406', '407', '408', '410', '411', '412', '413', '414', '417', '419', '420', '421', '422', '423', '424', '425', '426', '427', '428', '429', '431', '432', '433', '434', '435', '436', '437', '438', '439', '440', '441', '442', '443', '444', '445', '447', '448', '449', '450', '451', '453', '454', '455', '456', '457', '458', '459', '460', '461', '462', '463', '464', '465', '466', '467', '468', '469', '470', '471', '473', '474', '475', '476', '477', '478', '479', '480', '481', '482', '483', '484', '485', '486', '487', '488', '489', '490', '491', '492', '493', '494', '495', '496', '497', '498', '499']\n"
     ]
    }
   ],
   "source": [
    "from arch.bootstrap import StepM\n",
    "\n",
    "stepm = StepM(bm_losses, model_losses)\n",
    "stepm.compute()\n",
    "print('Model indices:')\n",
    "print([model.split('.')[1] for model in stepm.superior_models])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "better_models = pd.concat([model_losses.mean(0), model_losses.mean(0)], 1)\n",
    "better_models.columns = ['Same or worse', 'Better']\n",
    "better = better_models.index.isin(stepm.superior_models)\n",
    "worse = np.logical_not(better)\n",
    "better_models.loc[better, 'Same or worse'] = np.nan\n",
    "better_models.loc[worse, 'Better'] = np.nan\n",
    "fig = better_models.plot(style=['o', 's'], rot=270)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Model Confidence Set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model confidence set takes a set of **losses** as its input and finds the set which are not statistically different from each other while controlling the familywise error rate.  The primary output is a set of p-values, where models with a pvalue above the size are in the MCS.  Small p-values indicate that the model is easily rejected from the set that includes the best.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MCS P-values\n",
      "            Pvalue\n",
      "Model name        \n",
      "model.60     0.000\n",
      "model.80     0.001\n",
      "model.140    0.003\n",
      "model.40     0.004\n",
      "model.20     0.004\n",
      "model.100    0.004\n",
      "model.120    0.008\n",
      "model.0      0.008\n",
      "model.220    0.029\n",
      "model.260    0.109\n",
      "model.160    0.136\n",
      "model.240    0.136\n",
      "model.200    0.136\n",
      "model.180    0.378\n",
      "model.320    0.475\n",
      "model.420    0.551\n",
      "model.400    0.651\n",
      "model.360    0.846\n",
      "model.340    0.854\n",
      "model.280    0.854\n",
      "model.460    0.854\n",
      "model.380    0.854\n",
      "model.300    0.854\n",
      "model.480    0.854\n",
      "model.440    1.000\n",
      "Included\n",
      "['160', '180', '200', '240', '260', '280', '300', '320', '340', '360', '380', '400', '420', '440', '460', '480']\n",
      "Excluded\n",
      "['0', '100', '120', '140', '20', '220', '40', '60', '80']\n"
     ]
    }
   ],
   "source": [
    "from arch.bootstrap import MCS\n",
    "\n",
    "# Limit the size of the set\n",
    "losses = model_losses.iloc[:, ::20]\n",
    "mcs = MCS(losses, size=0.10)\n",
    "mcs.compute()\n",
    "print('MCS P-values')\n",
    "print(mcs.pvalues)\n",
    "print('Included')\n",
    "included = mcs.included\n",
    "print([model.split('.')[1] for model in included])\n",
    "print('Excluded')\n",
    "excluded = mcs.excluded\n",
    "print([model.split('.')[1] for model in excluded])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "status = pd.DataFrame([losses.mean(0), losses.mean(0)],\n",
    "                      index=['Excluded', 'Included']).T\n",
    "status.loc[status.index.isin(included), 'Excluded'] = np.nan\n",
    "status.loc[status.index.isin(excluded), 'Included'] = np.nan\n",
    "fig = status.plot(style=['o', 's'])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
